Revisiting the Reflected Caustics Method: the Accurate Shape of the “Initial Curve”

Abstract

The shape of the “initial curve”, i.e. the locus of material points, which if properly illuminated provide (under specific conditions) the “caustic curve”, is explored. Adopting the method of complex potentials improved formulae for the shape of the “initial curve” are obtained. Application of these formulae for two typical problems, i.e. the mode-I crack and the infinite plate with a finite circular hole under uniaxial tension, indicates that the “initial curve” is in fact not a circular locus. It is either an open curve or a closed contour, respectively, the actual shape of which depends also on the in-plane displacement field.